Problem $3(10$ points$)$

An insulated piston$-$cylinder system is connected by a valve to a supply line of Neon at $500$ kPa and $400$ K $.$ Initially, the piston is fully retracted $($i$.$e$.,$ no gas in cylinder$).$ The valve is opened and the cylinder allowed to expand until it contains $1$ kg of Neon occupying a volume of $1m^3.$ The mass of the piston is negligible, the piston is free to move, and atmospheric pressure is $100$ kPa $.$ How much work is done by the piston on the surroundings, in kJ$?$

Problem $4(6$ points$)$

Is it theoretically possible for a heat pump with a coefficient of performance $($COP ${?}_{HP})$ of $10$ to maintain the indoor temperature of a house at comfortable temperature when the outdoor temperature is $-10F?$